From Chemical Rules to Term Rewriting

In this paper, rule-based programming is explored in the field of automated generation of chemical reaction mechanisms. We explore a class of graphs and a graph rewriting relation where vertices are preserved and only edges are changed. We show how to represent cyclic labeled graphs by decorated labeled trees or forests, then how to transform trees into terms. A graph rewriting relation is defined, then simulated by a tree rewriting relation, which can be in turn simulated by a rewriting relation on equivalence classes of terms. As a consequence, this kind of graph rewriting can be implemented using term rewriting. This study is motivated by the design of the GasEl system for the generation of kinetics reactions mechanisms. In GasEl, chemical reactions correspond to graph rewrite rules and are implemented by conditional rewriting rules in ELAN. The control of their application is done through the ELAN strategy language.     

Conditional Term Graph Rewriting with Indirect Sharing

For reasons of efficiency, term rewriting is usually implemented by term graph rewriting. In term rewriting, expressions are represented as terms, whereas in term graph rewriting these are represented as directed graphs. Unlike terms, graphs allow a sharing of common subexpressions. In previous work, we have shown that conditional term graph rewriting is a sound and complete implementation for a certain class of CTRSs with strict equality, provided that a minimal structure sharing scheme is used. In this paper, we will show that this is also true for two different extensions of normal CTRSs. In contrast to the previous work, however, a non-minimal structure sharing scheme can be used. That is, the amount of sharing is increased.     

含假结RNA二级结构类的图语法

用最小自由能法预测RNA二级结构是NP困难问题,其根本原因是假结的存在。近几年的预测算法都针具有一定结构特征的假结寻找多项式时间算法进行预测。论文针对RNA二级结构图提出一种图语法,该语法由初始结构图集和重写规则集构成,用重写规则在初始结构图上的不断重写得到的结构图都是该语法的语言。分析了5个主流RNA二级结构预测算法的目标集,给出它们的图语法,使得目标集的结构特征一目了然,目标集间的真包含关系也通过图语法直观地体现出来。     

Structure and Properties of Traces for Functional Programs

The tracer Hat records in a detailed trace the computation of a program written in the lazy functional language Haskell. The trace can then be viewed in various ways to support program comprehension and debugging. The trace was named the augmented redex trail. Its structure was inspired by standard graph rewriting implementations of functional languages. Here we describe a model of the trace that captures its essential properties and allows formal reasoning. The trace is a graph constructed by graph rewriting but goes beyond simple term graphs. Although the trace is a graph whose structure is independent of any rewriting strategy, we define the trace inductively, thus giving us a powerful method for proving its properties.     

Bisimilarity in Term Graph Rewriting

We present a survey of confluence properties of (acyclic) term graph rewriting. Results and counterexamples are given for different kinds of term graph rewriting; besides plain applications of rewrite rules, extensions with the operations of collapsing and copying, and both operations together are considered. Collapsing and copying together constitute bisimilarity of term graphs. We establish sufficient conditions for—and counterexamples to—confluence, confluence modulo bisimilarity, and the Church–Rosser property modulo bisimilarity. Moreover, we address rewriting modulo bisimilarity, that is, rewriting of bisimilarity classes of term graphs.     

A kernel language for programmed rewriting of (hyper)graphs

The paper presents a formalism for rewriting (hyper)graphs in a controlled manner. This formalism is essentially a simple programming language with productions, that is rewriting rules, playing the role of basic instructions. Programs in this language are built from productions by means of rather standard constructors, including a parallel composition. They may contain parameters to point to specific elements of graphs to which they are supposed to be applied. Programs are intended to describe how to transform a graph and a valuation of parameters in this graph in order to reach a resulting graph and a resulting valuation of parameters.     

A kernel language for programmed rewriting of (hyper)graphs

The paper presents a formalism for rewriting (hyper)graphs in a controlled manner. This formalism is essentially a simple programming language with productions, that is rewriting rules, playing the role of basic instructions. Programs in this language are built from productions by means of rather standard constructors, including a parallel composition. They may contain parameters to point to specific elements of graphs to which they are supposed to be applied. Programs are intended to describe how to transform a graph and a valuation of parameters in this graph in order to reach a resulting graph and a resulting valuation of parameters. Received July 13, 1994 / May 2, 1995     

Structural Properties of Context-Free Sets of Graphs Generated by Vertex Replacement

We establish that a Vertex Replacement set of graphs, i.e., a set of graphs generated by a C-edNCE or, equivalently, by a separated handle rewriting graph grammar is Hyperedge Replacement, i.e., is generated by a hyperedge replacement graph grammar, iff its graphs do not contain arbitrary large complete bipartite graphs K_{n, n} as subgraphs. Another equivalent condition is that its graphs have a number of edges that is linearly bounded in terms of the number of vertices. These properties are decidable by means of an appropriate extension of the theorem by Parikh that characterizes the commutative images of context-free languages. We extend these results to hypergraphs.     

嵌入一致图语法的依赖图

图语法将字符串上的形式文法扩充为图上的形式文法,提供一种能够使用精确的数学方法来模拟图变换的机制.提出了几种新的基于一致图语法的方法来表示控制流图、数据流图、控制数据流图、二分图和超图,并说明如何通过图重写来自动生成依赖图并挖掘并行性,从而协助并行编译器和并行语言的设计和实现.     

Parallel complexity of signed graphs for gene assembly in ciliates

We consider a graph-based model for the study of parallelism in ciliate gene assembly, where a signed graph is associated to each micronuclear gene and the gene assembly is modeled as a graph rewriting process. A natural measure of complexity for gene assembly counts the minimal number of parallel steps needed to reduce the associated signed graph. We investigate the complexity of several classes of the graphs, so far found graphs of parallel complexity up to six. The general problem of whether there exists a finite upper bound for the graph parallel complexity still remains open.     

Representing graph families with edge grammars

An edge grammar is a formal mechanism for representing families of related graphs (binary trees, hypercubes, meshes, etc.). Given an edge grammar, larger graphs in the family are derived from simple basis graphs using edge rewriting rules. A drawback to many graph grammars is that they cannot represent some important, highly regular graph families such as the family of shuffle-exchange graphs. Edge grammars, however, exist for all “computable” graph families, and simple edge grammars exist for most regular graph families. In this paper, we define and illustrate edge grammars and analyze them in the context of formal language theory. Our results include hierarchy and decidability properties. Because this work originally was motivated by a need to represent graph families found in parallel computation, the application of edge grammars in this context is also discussed.     

Modelling Calculi with Name Mobility using Graphs with Equivalences

In the theory of graph rewriting, the use of coalescing rules, i.e., of rules which besides deleting and generating graph items, can coalesce some parts of the graph, turns out to be quite useful for modelling purposes, but, at the same time, problematic for the development of a satisfactory partial order concurrent semantics for rewrites. Rewriting over graphs with equivalences, i.e., (typed hyper)-graphs equipped with an equivalence over nodes provides a technically convenient replacement of graph rewriting with coalescing rules, for which a truly concurrent semantics can be easily defined. The expressivity of such a formalism is tested in a setting where coalescing rules typically play a basic role: the encoding of calculi with name passing as graph rewriting systems. Specifically, we show how the (monadic fragment) of the solo calculus, one of the dialect of those calculi whose distinctive feature is name fusion, can be encoded as a rewriting system over graph with equivalences.     

A Higher-Order Calculus for Graph Transformation

This paper presents a formalism for defining higher-order systems based on the notion of graph transformation (by rewriting or interaction). The syntax is inspired by the Combinatory Reduction Systems of Klop. The rewrite rules can be used to define first-order systems, such as graph or term-graph rewriting systems, Lafont's interaction nets, the interaction systems of Asperti and Laneve, the non-deterministic nets of Alexiev, or a process calculus. They can also be used to specify higher-order systems such as hierarchical graphs and proof nets of Linear Logic, or to specify the operational semantics of graph-based languages.     

On the reachability of a version of graph-rewriting system

In this paper, we consider a problem on the reachability of a version of graph-rewriting system. It deals with 3-regular graphs with states for the vertices. They differ from ordinary graphs so that a cyclic order of the edges is assigned on each vertex. Graphs are rewritten with a rule set of graph rewriting. For any two such connected graphs with at least four vertices of distinct states, we show that there exists a rule set that rewrites one to the other.     

ParaGraph: Graph editor support for parallel programming environments

We report here on a graph editor, ParaGraph, that supports massively parallel programming. It provides a flexible mechanism for the concise specification of families of annotated graphs, addressing the problems of user annotation and scale independent graph manipulation. ParaGraph currently serves as the basis for tools supporting communication abstractions in program specification and debugging. Its foundation in an extended form of aggregate rewriting graph grammars makes its adaptation to other parallel programming environments straightforward.The Parallel Programming Environments Project at the University of Massachusetts is supported by the Office of Naval Research under Contract N000014-84-K-0647 and by the National Science Foundation under Grants DCR-8500332 and CCR-8712410.     

On graph rewriting,reduction, and evaluation in the presence of cycles

We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.’s mechanical program derivations from the world of terms to the world of cyclic graphs. We also outline how to inter-derive a third style of graph reduction: a graph evaluator.     

Combining overlap and containment for gene assembly in ciliates

Gene assembly in ciliates is an intricate biological process that has been studied formally and modeled through string and graph rewriting systems. Recently, a restriction of the general (intramolecular) model, called simple gene assembly, has been introduced. This restriction has subsequently been defined as a string rewriting system. We show that, by extending the notion of overlap graph to also represent containment, it is possible to define an equivalent graph rewriting system for two of the three types of rules that make up simple gene assembly. It turns out that this graph rewriting system is often less involved to study than its corresponding string rewriting system. We illustrate this by giving characterizations of the ‘power’ of both types of graph rewriting rules. Also, a first step is made towards a characterization of the “extended overlap graphs”.     

Reachability Problems on Regular Ground Tree Rewriting Graphs

We consider the transition graphs of regular ground tree (or term) rewriting systems. The vertex set of such a graph is a (possibly infinite) set of trees. Thus, with a finite tree automaton one can represent a regular set of vertices. It is known that the backward closure of sets of vertices under the rewriting relation preserves regularity, i.e., for a regular set T of vertices the set of vertices from which one can reach T can be accepted by a tree automaton. The main contribution of this paper is to lift this result to the recurrence problem, i.e., we show that the set of vertices from which one can reach infinitely often a regular set T is regular, too. Since this result is effective, it implies that the problem whether, given a tree t and a regular set T, there is a path starting in t that infinitely often reaches T, is decidable. Furthermore, it is shown that the problems whether all paths starting in t eventually (respectively, infinitely often) reach T, are undecidable. Based on the decidability result we define a fragment of temporal logic with a decidable model-checking problem for the class of regular ground tree rewriting graphs.     

A Path Following Algorithm for the Graph Matching Problem

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.